The jet breaks in the afterglow light curves of short gamma-ray bursts (SGRBs), rarely detected so far, are crucial for estimating the half-opening angles of the ejecta (θ _j) and hence the neutron star merger rate. In this work, we report the detection of jet decline behaviors in GRB 150424A and GRB 160821B, and find θ _j ∼ 0.1 rad. Together with five events reported before 2015 and three others “identified” recently (GRB 050709, GRB 060614, and GRB 140903A), we have a sample consisting of nine SGRBs and one long-short GRB with reasonably estimated θ _j. In particular, three Swift bursts in the sample have redshifts z ≤ 0.2, with which we estimate the local neutron star merger rate density to be or if the narrowly beamed GRB 061201 is excluded. Inspired by the typical θ _j ∼ 0.1 rad found currently, we further investigate whether the off-beam GRBs (in the uniform jet model) or the off-axis events (in the structured jet model) can significantly enhance the GRB/GW association. For the former, the enhancement is at most moderate, while for the latter the enhancement can be much greater and a high GRB/GW association probability of ∼10% is possible. We also show that the data of GRB 160821B may contain a macronova/kilonova emission component with a temperature of ∼3100 K at ∼3.6 days after the burst and more data are needed to ultimately clarify.

Fast radio bursts (FRBs) are radio bursts characterized by millisecond durations, high Galactic latitude positions, and high dispersion measures. Very recently, the cosmological origin of FRB 150418 has been confirmed by Keane et al., and FRBs are now strong competitors as cosmological probes. The simple sharp feature of the FRB signal is ideal to probe some of the fundamental laws of physics. Here we show that by analyzing the delay time between different frequencies, the FRB data can place stringent upper limits on the rest mass of the photon. For FRB 150418 at z = 0.492, one can potentially reach m γ ≤ 5.2 × 10 − 47 g, which is 10²⁰ times smaller than the rest mass of electron and is about 10³ times smaller than that obtained using other astrophysical sources with the same method.